using high-dimensional image models to perform highly...
TRANSCRIPT
Using High-Dimensional Image Models to Perform
Highly Undetectable Steganography
Tomá² Pevný1, Tomá² Filler2, Patrick Bas3
1CTU, Prague, Czech Republic2 SUNY, Binghamton, USA
3Lagis, Lille, France
29th June 2010
T. Pevný, T. Filler, P. Bas | HuGO � Highly Undetectable steGO 1/20
Outline
1 Motivation
2 Minimizing the distortion function
3 Designing the distortion function
4 Experimental veri�cation
5 Conclusion
T. Pevný, T. Filler, P. Bas | HuGO � Highly Undetectable steGO 2/20
Outline
1 Motivation
2 Minimizing the distortion function
3 Designing the distortion function
4 Experimental veri�cation
5 Conclusion
T. Pevný, T. Filler, P. Bas | HuGO � Highly Undetectable steGO 3/20
Steganography
Practical steganography for digital media
modi�es the cover objects to convey the message.
makes changes as undetectable as possible.
Distortion function
any function D : X ×X → [0,∞].
correlates with detectability.
is minimized during embedding.
T. Pevný, T. Filler, P. Bas | HuGO � Highly Undetectable steGO 4/20
Additive distortion function
D(x ,y) =n
∑i=1
ρi |xi − yi |
|xi − yi | ≤ 1,
ρi cost of changing one pixel (embedding impact)
Aditivity implies that embedding changes do not interact.
T. Pevný, T. Filler, P. Bas | HuGO � Highly Undetectable steGO 5/20
Separational principle
Theorema
If we want to communicate m bits in n elements (pixels), than the
minimal expected distortion is
Dmin(m,n,ρ) =n
∑i=1
piρi ,
where pi is the probability of changing the ith pixel,
pi =e−λρi
1+ e−λρi
.
The parameter λ is obtained by solving ∑ni=1H(pi ) = m.
aJ. Fridrich and T. Filler, Practical Methods for Minimizing Embedding Impact in
Steganography, 2007
T. Pevný, T. Filler, P. Bas | HuGO � Highly Undetectable steGO 6/20
Corollary of the theorem
Corrolary
Design of the steganographic algorithm boils down to
the design of an additive distortion function D, orthe setting embedding costs ρi .
Allows to compare additive distortion functions.
Practical algorithms approaching the distortion bound existsa.
aT. Filler, J. Fridrich, and J. Judas, Minimizing embedding impact in steganography
using Trellis-Coded Quantization, 2010
T. Pevný, T. Filler, P. Bas | HuGO � Highly Undetectable steGO 7/20
Outline
1 Motivation
2 Minimizing the distortion function
3 Designing the distortion function
4 Experimental veri�cation
5 Conclusion
T. Pevný, T. Filler, P. Bas | HuGO � Highly Undetectable steGO 8/20
Designing the distortion function
Distortion function
D(x,y) = ‖f (x)− f (y)‖=d
∑j=1
wj |fj(x)− fj(y)|
d � number of features
Additive approximation
D ′(x,y) =n
∑i=1
D(x,yix)|xi − yi |
n � number of pixels
T. Pevný, T. Filler, P. Bas | HuGO � Highly Undetectable steGO 9/20
Model Correction
+1
-1
+1
-1
+1
-1
+1
-1
no change change pixel
Compensates the suboptimality caused by approximating D(x ,y) byD ′(x ,y).
T. Pevný, T. Filler, P. Bas | HuGO � Highly Undetectable steGO 10/20
Outline
1 Motivation
2 Minimizing the distortion function
3 Designing the distortion function
4 Experimental veri�cation
5 Conclusion
T. Pevný, T. Filler, P. Bas | HuGO � Highly Undetectable steGO 11/20
Features of the model
d3
d2
d1
Distortion function
D(x,y) =T
∑d1,d2,d3=−T
wd1,d2,d3
∣∣fd1,d2,d3(x)− fd1,d2,d3(y)∣∣f →d1,d2,d3 � # of di�erences (d1,d2,d3) between neighboring pixels
T. Pevný, T. Filler, P. Bas | HuGO � Highly Undetectable steGO 12/20
Setting the weights
−60
6
−60
6
0
5 · 10−2
0.1
d2d1
Mean of CX,→d1d2
feature
00
0
0.5
1
d2d1
w(d1, d2) =[√
d21 + d2
2 + σ]−γ
T. Pevný, T. Filler, P. Bas | HuGO � Highly Undetectable steGO 13/20
Outline
1 Motivation
2 Minimizing the distortion function
3 Designing the distortion function
4 Experimental veri�cation
5 Conclusion
T. Pevný, T. Filler, P. Bas | HuGO � Highly Undetectable steGO 14/20
Detectability by Spam
0 0.2 0.4 0.6 0.8 10
0.2
0.4
0.1
0.3
0.5
noModelCorrect.
withModelCorrect.
HuGO
ternary LSB match.
simulatedSTC h = 10
Relative payload (bpp)
Err
or
PE
�xed size 512×512
images
PE = min1
2
(PFp +PFn
)SVMs with Gaussian
kernel.
T. Pevný, T. Filler, P. Bas | HuGO � Highly Undetectable steGO 15/20
Detectability by feature sets
0 0.2 0.4 0.6 0.8 10
0.2
0.4
0.1
0.3
0.5 WAMSPAM 1st
SPAM 2nd
CDF
ternary LSB matching
HuGO
Relative payload (bpp)
Err
or
PE
T. Pevný, T. Filler, P. Bas | HuGO � Highly Undetectable steGO 16/20
HuGO, where did you hide the message?
Fig: 0.25 bits per pixel Fig: 0.50 bits per pixel
T. Pevný, T. Filler, P. Bas | HuGO � Highly Undetectable steGO 17/20
Outline
1 Motivation
2 Minimizing the distortion function
3 Designing the distortion function
4 Experimental veri�cation
5 Conclusion
T. Pevný, T. Filler, P. Bas | HuGO � Highly Undetectable steGO 18/20
Conclusion
We presented a methodology to design a steganographic
algorithm by applying state of the art principles:
separate distortion function from codinguse of high-dimensional model (107 features).
The practical realization, HuGO allows the embedder to hide
7× longer message than LSB matching at the same level of
security.
T. Pevný, T. Filler, P. Bas | HuGO � Highly Undetectable steGO 19/20
Do you want be the BOSS?
B O S SBreak Our Steganographic SystemBreak Our Steganographic System
Steganalytic challenge is coming up in June 2010!
1000 images, 500 with a hidden message
Guess which ones!
http://boss.gipsa-lab.grenoble-inp.fr
T. Pevný, T. Filler, P. Bas | HuGO � Highly Undetectable steGO 20/20